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A061687 Generalized Bell numbers. 3


%S 1,1,33,8506,9483041,33056715626,293327384637282,5747475089121405893,

%T 224054040415856117594913,16044797009828490454609378642,

%U 1981736776623437001042672440089658,401147408702290404750740714717055504773,127573929384655691416638350563783440408133922

%N Generalized Bell numbers.

%H Alois P. Heinz, <a href="/A061687/b061687.txt">Table of n, a(n) for n = 0..117</a>

%H J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/SIXDENIERS/bell.html">Extended Bell and Stirling Numbers From Hypergeometric Exponentiation</a>, J. Integer Seqs. Vol. 4 (2001), #01.1.4.

%p a:= proc(n) option remember; `if`(n=0, 1,

%p add(binomial(n, k)^6*(n-k)*a(k)/n, k=0..n-1))

%p end:

%p seq(a(n), n=0..15); # _Alois P. Heinz_, Nov 07 2008

%t a[n_] := a[n] = If[n == 0, 1, Sum[Binomial[n, k]^6*(n-k)*a[k]/n, {k, 0, n-1}]]; Table[a[n], {n, 0, 15}] (* _Jean-Fran├žois Alcover_, Mar 19 2014, after _Alois P. Heinz_ *)

%Y Column k=6 of A275043.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jun 18 2001

%E More terms from _Alois P. Heinz_, Nov 07 2008

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Last modified January 19 00:40 EST 2020. Contains 331030 sequences. (Running on oeis4.)